Variation of height in an isogeny class over a function field

Richard Griffon; Samuel Le Fourn; Fabien Pazuki

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arXiv · 2503.14318

Variation of height in an isogeny class over a function field

Richard Griffon·Samuel Le Fourn·Fabien Pazuki

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Abstract

We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any characteristic). We also prove a parallelogram inequality for abelian varieties in this context, and deduce corollaries of these results.

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Richard Griffon, Samuel Le Fourn, Fabien Pazuki. 2025-03-18. Variation of height in an isogeny class over a function field. https://arxiv.org/abs/2503.14318

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